A U M -    
MANTRA – 8
so.ayam  atmadhyaksharam  onkaro.adhimatram  pada matra matrashcha pada akara ukaro makara  iti .. 8..
The  same Atman which has been described above as having four quarters, is  again AUM from the point of view of syllables (letters – aksharam). The  AUM with parts is viewed from the standpoint of sounds (letters, matras).  The quarters are the letters (parts) and the letters are the quarters. The  letters here are A, U, and M.
The  word AUM which has been explained before as Atman having four quarters  is again explained as the same Atman from the standpoint of syllable  where prominence is given to the name. What is the syllable? It is AUM. It is  that word AUM which being divided into parts, is viewed from the standpoint of  letters. How? Those which constitute the quarters of the Atman are the  letters of AUM. What are they? They are A (akaara), U (ukaara),  and M (makaara).
Earlier  it was said that the Self can be seen in four states or quarters (padas); visva – the waking state, taijasa – the dream state, prajna – the deep sleep state and turiya – pure consciousness. Turiya is the  real nature of the Self.
The  first three states (padas) of the Self are represented by the three  letters (matras) A U M. Hence this mantra says that the padas and  the matras are the same. Turiya is beyond description; so it is amatra- beyond the matras.
A doubt  may naturally arise as to why this repetition of explaining the same idea about Atman, though in different ways. The reason is that those who cannot  enter upon philosophical reflection regarding the Supreme Reality as given in  the previous mantras are advised to concentrate on AUM as the symbol of  the Ultimate Reality.
MANTRA – 9
jagaritasthano  vaishvanaro.akarah  prathama matra.a.apter  adimattvad.h va.a.apnoti  ha   vai  sarvan.h  kaman   adish  cha bhavati   ya evam veda .. 9..
He  who is Vaisvanara, having for its sphere of activity the waking state, is A (A-kaara),  the first letter of AUM on account of its all –pervasiveness or on account of  being the first. One who knows this attains to the fulfillment of all desires  and becomes the foremost among all.
In this  mantra the points of resemblance between the waking state and the first letter  of AUM (akaara - A) are elucidated. That which is Vaisvanara,  whose sphere of activity is the waking state, is the first letter of AUM. Their  common features are tabulated as under.
  
    | Sr No | Waking State | First letter – akaara (A) - A  | 
  
    | 1 | Pervasiveness –    Entire Universe is pervaded by Vaisvanara Atman whose symbol is waking    state. Knowledge of all other states is possible only from the waking    state. The three states constitute our entire experience of the universe. Therefore    the waking state pervades the whole of the universe. | All sounds are    pervaded by ‘A’. It is present in all sounds because when a man wants to    utter any sound, the very opening of his mouth produces (audibly or    inaudibly) the sound ‘A’. | 
  
    | 2 | Waking sate is    the beginning of the other states. Our common experience tells us that the    states of dream and deep sleep are preceded by the waking state which is    therefore the first of the three states.    | ‘A’ is the    first letter of the alphabet; it is the first of the three letters    constituting AUM; it is the first of all sounds. Hence it is called the beginning    because no other sound or letter precedes ‘A’.  In the Bhagavad Gita (10.33) also Bhagavan    says that among the letters, He is the letter’A’ (aksharaanaam    akaaro'smi)  | 
The  mantra says that the one who knows the identity of the two as described above  has all his desires fulfilled and becomes the chief of the great; this  enumeration of merits is for the purpose of inducing the seeker to understand  the meaning of AUM.
MANTRA – 10
svapnasthanas  taijasa   ukaro  dvitiya  matrotkarshat.h  ubhayatvadvotkarshati  ha vai   jnanasantati.n  samanashcha  bhavati   nasyabrahma-vit-kule  bhavati  ya evam veda .. 10..
Taijasa,  whose sphere of activity is the dream state, is U (U- kaara), the second letter  of AUM on account of superiority or on account of being in between the two. He  who knows this attains to a superior knowledge, is treated equally by all alike  and finds no one in his line who is not a knower of Brahman. 
In this  mantra the points of resemblance between the dream state and the second letter  of AUM (ukaara – U) are elucidated. That which is taijasa, whose  sphere of activity is the dream state, is the second letter of AUM. Their  common features are tabulated as under.
  
    | Sr No | Dream State | Second letter – ukaara (U) -  %  | 
  
    | 1 | Taijasa or Atman functioning through the dream state is said to be superior to Vaisvanara    because he perceives ideas whereas the latter sees only gross objects.  | As the letter    ‘U’ comes after ‘A’, it is said to be superior as in the case of a dignitary showing    his appearance only after the lesser ranks pass through first. | 
  
    | 2 | Taijasa is in    the middle between Visva and Prajna. | As the letter    ‘U’ is between ‘A’ and ‘M’, the dream state is between waking and deep sleep    states.  | 
The  mantra says that the one who knows the identity of the two as described above  attains superior knowledge, is treated alike by all in the society, and that  all the successors in his family will be knowers of Brahman or will be having  full knowledge of Brahman which only means that his lineage will remain pure  without any varna sankara or adulteration.
MANTRA – 11
sushuptasthanah  prajno   makaras  tritiya matran  miter   apiter  va
    minoti  ha   va  idam  sarvam   apitish  cha  bhavati   ya evam  veda .. 11..
Prajna, whose sphere is deep sleep, is ‘M’ (M - kaara), the third  letter of AUM, because it is both the measure and that wherein all becomes one.  One who knows this identity of prajna and M is able to measure all i.e. realizes  the real nature of the world, and also comprehends all within himself.
In this  mantra the points of resemblance between the deep sleep state and the third  letter of AUM (makara – M) are elucidated. That which is prajna,  whose sphere of activity is the deep sleep state, is the third letter of AUM.  Their common features are tabulated as under.
  
    | Sr No | Deep Sleep State | Third letter – ma kaara (M) - m | 
  
    | 1 | In the deep    sleep state of consciousness, both the waking state and the dream state    experiences seem to enter into a mass of homogeneous awareness and on waking    up out of this undifferentiated mass of consciousness i.e. the sleep state,    the waking and dream states seem to emerge out separately (just as in a    measuring glass liquids are poured in for measuring and poured out after    measuring).  | In the process    of repeated pronouncing of the sound AUM, the sounds ‘A’and ‘U’ seem to merge    in and emerge out of the sound ‘M’. In this manner    both ‘M’ and deep sleep state are compared to a measuring glass in the    mantra.
 | 
  
    | 2 | In both deep    sleep state and the third letter of AUM, the earlier plurality and    differences merge themselves to become one-whole. | 
He who  realizes this identity between the two is able to measure all things in the  sense that he can discriminate between things and to understand and judge the  happenings both within and outside him. No situation is beyond his grasp or  understanding.